Pawn Structure Classification Codes
I'm currently working on a new classification of chess openings. I post here a summary of the beginning of my book Coherent Mathematical Classification of Chess Openings, Pawn Structures and PSCC Codes in preparation. Any comments, remarks, suggestions etc. are welcome! 
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1. Pawn height
The pawn height of a white (resp. black) pawn on the board with coordinates (x,y) is y-2 (resp. 7-y). It's the vertical distance from its original position. By definition, the height of a taken or promoted pawn is equal to 6. The total height h of a chess position is the sum of heights of all 16 white and black pawns. So, the maximal height of a pawnless endgame is equal to 16x6=96. The height is also naturally divided in white and black parts h=h1+h2 where h1, h2 =< 48. Heights 32 and 64 approximately divide chess games into 3 parts: opening, middle game and endgame.
2. PSCC codes
Pawn Structure Classification Codes are written as follows. The PSCC code of the initial position IP or a game without pawn mouvements is I. Otherwise, the general form of a PSSC code is
[6*][5*][4*][3*][2*][1*}[0*]
where * stands for words in capital and small letters containing A,...,H (resp. a,...,h). These letters describe advanced pawns, capital for white and small for black, and corresponding number is equal to their height. For example, the Sicilian: Alapin opening 1. e4 e5 2. c3 has height 5 and PSCC code 2Ec1C. Files without pawns are described by the expression 6* or 0* depending on the height. For instance, Scandinavian game 1. e4 d5 2. exd5 Qxd5 has height 12=6+6 and PSCC code 6Ed. Doubled pawns are indicated by an additional * symbol. Let's take Ruy Lopez: Exchange variation 1. e4 e5 2. Nf3 Nc6 3. Bb5 a6 4. Bxc6 dxc6 as an example. Its height is 6=2+4 and it is described by PSCC code 2Ee1ac*0d (here * indicates that the pawn on c6 is doubled). By erasing all letters in a PSCC code we obtain the numerical code (NC) of the position. Notice that PSCC codes describe chess positions while chess games correspond to sequences of such codes.
2. Oriented graph G of pawn structures
Admissible pawn structures are vertices of this graph. Consider two vertices
S1 and S2. They are connected by an arrow if there is a position P2 with structure S2 that can be obtained from a position P1 with structure S1 in 1 ply. The graph G is a ramified tree with the unique root I and the unique treetop 6ABCDEFGHabcdefgh
of height 96=48+48. How many branches (arrows) go from the root to the stratum
of height 1, i.e. what is the number of pawn structures of level 1? There are 8 structures of height 1+0: 1A,...,1H as well as 8 structures of height 0+1: 1a,...,1h.
4. Ramified core of G
Let's consider the set of all master games. We say that a given pawn structure belong to the ramified k-core if it appears in, at least, k>1 games. In this book we will indicate PSCC codes for 100-core games (k=100). The number of games will be taken from the chess.com database. Aproximative numerical evaluations of chess positions are deduced from the chessOK database and chess.com explorer.
5. Games of height 0 and transitions
The PSCC code of such games is I. The initial position itself will be denoted IP. We indicate all transitions to positions belonging to the ramified 100-core of master
games.
I: IP [A00, +0.1/+0.15]
--->(1.a3) 1A Anderssen's opening [A00, +0.0], h=1+0.
--->(1.b3) 1B NLA [A01, -0.05/-0.00], h=1+0.
--->(1.c3) 1C Saragossa opening [A00, -0.05], h=1+0.
--->(1.d3) 1D Mieses opening [A00, -0.05/-0.00], h=1+0.
--->(1.e3) 1E Van't Kruijs opening [A00, +0.05], h=1+0.
--->(1.g3) 1G Benko's opening [A00, +0.0], h=1+0.
--->(1.b4) 2B Sokolsky opening [A00, -0.2 ], h=2+0.
--->(2.c4) 2C English opening [A10, +0.05/+0.1], h=2+0.
--->(2.d4) 2D QP [A40, +0.1/+0.15], h=2+0.
--->(2.e4) 2E KP [B00, +0.1/+0.15], h=2+0.
--->(2.f4) 2F Bird's opening [A02, -0.1/-0.05], h=2+0.
--->(2.g4) 2G Grob opening {A00, -0.4/-0.3], h=2+0.
I: 1.Nc3 Dunst [A00, +0.0/+0.1] --> 1g, 2c, 2d, 2e Reversed Nimzo.
I: 1.Nc3 Nf6 Dunst [A00, +0.1] --> 2d QP: Indian, 2e Alekhine.
I: 1.Nf3 Réti [A04, +0.1/+0.2] --> 1b Réti: QF, 1c Réti: Slav, 1d Réti: Pirc, 1e, 1g
Réti: KF, 2b Réti: Polish, 2c Réti: Sicilian, 2d, 2f Réti: Dutch.
I: 1.Nf3 Nc6 Réti: Black Mustang [A04, +0.2/+0.3] --> 1G Benko, 2C Anglo-Lithuanian, 2D Mikenas, 2E QP: Nimzo.
I: 1.Nf3 Nf6 Réti: Symm [A05, +0.1/+0.2] --> 1B Réti: NLA, 1D Mieses, 1E Réti: Quiet,
1G Réti: KIA, 2B Sokolsky: Zukertort, 2C Anglo-Indian: KK, 2D Indian: KK.
Abbreviations:
IP = Initial Position
KF = Kingside Fianchetto
KIA = King's Indian Attack
KK = King's Knight
KP = King's Pawn
NLA = Nimzo-Larsen Attack
QF = Queenside Fianchetto
QP = Queen's Pawn
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